The present invention relates generally to a scanning optical system, and more particularly to a scanning optical system comprising optical deflection means for deflecting light coming from a light source, so that the surface to be scanned is two-dimensionally scanned.
Exemplary prior scanning optical systems are shown in FIGS. 10 and 11. The scanning optical system shown in FIG. 10 (JP-A 08-327926) uses a condensing optical system comprising collimator lens 52, slit 53 and cylindrical lens 54, through which light leaving light source 51 is collimated and guided to rotary polygon mirror 55. The light reflected and deflected at rotary polygon mirror 44 is directed to image-formation lens 56 composed of two lens elements, so that image-formation surface 57 is subjected to one-dimensional scanning.
The scanning optical system shown in FIG. 11 (JP-A 08-146320) uses collimator lens 62 for collimating light leaving light source 61 into a parallel light beam, which is then reflected and deflected by deflection means 63, so that the surface 65 to be scanned is subjected to two-dimensional scanning by image-formation means 64.
However, the optical system of FIG. 10, because of being constructed of a considerable number of optical elements, places strict limitations on the precision of assembling and adjustment to achieve the necessary optical performance, and incurs some added expenses as well. For the optical system of FIG. 11, on the other hand, nothing is disclosed about its specific arrangement.
Having been accomplished to provide a solution to such problems with the prior art as mentioned above, the present invention has for its object to provide a scanning optical system of small size, which is constructed of a reduced number of optical elements.
According to the first aspect of the present invention, the aforesaid object is achieved by the provision of a scanning optical system comprising optical deflection means for deflecting light from a light source to scan the surface to be scanned and an image-formation optical system for focusing the light deflected by said optical deflection means on the surface to be scanned, thereby forming an image thereon, characterized in that:
said image-formation optical system comprises an optical member wherein a surface thereof having optical power and located nearest to the surface to be scanned has a transmission function alone, and
said optical member comprises two or more reflecting surfaces, each of which has optical power and includes at least one rotationally asymmetric surface decentered with respect to an axial chief ray.
This scanning optical system is exemplified by Examples 1 to 6 given later.
The advantages (effects and actions) of the scanning optical system according to the first aspect of the invention are now explained. By allowing the optical member to comprise two or more reflecting surfaces, each of which has optical power and includes at least one rotationally asymmetric surface decentered with respect to an axial chief ray (hereinafter called the decentered, rotationally asymmetric surface), the xe2x80x9cturn-backxe2x80x9d effect is obtained so that the size of the optical system can be much more reduced than ever before. The reflecting surfaces of optical power, because of having both a lens action and a deflection action, contribute significantly to size reductions.
Referring here to an optical system comprising a rotationally symmetric reflecting surface having optical power and decentered with respect to an axial chief ray, light rays strike obliquely on that reflecting surface. Even with axial rays, accordingly, aberrations such as comas and astigmatisms are produced due to decentration. Such decentration aberrations may be corrected by configuring this reflecting surface in the form of a rotationally asymmetric surface as contemplated herein.
A problem with a general scanning optical system is that when light deflected by optical deflection means is entered on a decentered, rotationally symmetric surface, it is impossible to ensure any linear scan capability. However, this linear scan capability can be ensured by configuring the reflecting surface of an image-formation optical system in the form of a rotationally asymmetric reflecting surface.
Further, the use of the rotationally asymmetric surface enables the image-formation optical system to be formed of a two-dimensional f arcsine xcex8 lens or a two-dimensional fxcex8 lens. Consequently, the surface to be scanned can be easily subjected to constant-speed, two-dimensional scanning.
When optical deflection means with the angle of deflection changing linearly, such as a rotary polygon mirror, is used, an fxcex8 lens may be used as the image-formation optical system capable of producing minus distortions. Consequently, the surface to be scanned can be scanned at a constant speed. When optical deflection means with the angle of deflection changing sinusoidally, such as a galvanometer mirror, is used, the image-formation optical system may be configured as an f arcsine xcex8 lens by allowing it to produce distortions depending on the magnitude of the angle of deflection (plus distortion when the angle of deflection is small, and minus distortion when the angle of deflection is large). Consequently, the surface to be scanned can be subjected to constant-speed scanning.
In this case, the surface of the image-formation optical system, which has optical power and is located nearest to the surface to be scanned, is effective for correction of distortions because there is a large difference in light ray position between the angles of view, with a light beam of reduced diameter. It is noted that the function of this surface on correction of distortions becomes worse if this surface is designed to have a function of transmitting light and a function of reflecting light or to have a function of transmitting light and a function of transmitting light, because some restrictive conditions are placed on such a surface. It is noted that the surface formed of a single surface and designed to produce a plurality of optical functions will hereinafter called a combined surface. Thus, if that surface is designed to have a single optical function alone, i.e., only a transmission function as contemplated herein, it is then possible to make effective correction for distortions. It is also easy to ensure the angle of view.
According to the second aspect of the present invention, the scanning optical system of the first aspect is further characterized in that said optical member is configured in the form of a prism member.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. Generally speaking, a reflecting surface must be more strictly controlled in terms of decentration errors than a refracting surface, and so its adjustment on assembling is an onerous task. However, if the reflecting surface of the optical member is configured as one surface of the prism member, then this problem can be solved because the whole positioning of the reflecting surface becomes easy.
Light rays incident from the deflection means on the prism member are refracted at the entrance surface of the prism member, so that the heights of off-axis light rays incident on the subsequent surfaces can be kept low. It is thus possible to reduce the size of the optical system and achieve a larger angle of view as well. In addition, the height of light rays depending on the off-axis light rays becomes so low that comas or the like can be reduced.
According to the third aspect of the invention, the scanning optical system of the first aspect is further characterized in that said optical member comprises at least one surface which has a function of transmitting light and a function of reflecting light. This surface should preferably be defined by a surface other than that located nearest to the surface to be scanned.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. Since the two functions, transmission and reflection, occur at the same surface, the number of surfaces that form the image-formation system can be so reduced that it can be simplified and reduced in size. More preferably in this case, the reflection function should be total reflection function. When reflection at the combined surface is reflection at a reflecting film rather than total reflection, it is necessary to form the reflecting film for the reflecting surface at another position separate from a transmitting area for a transmitting surface, offering problems such as an increase in the size of the optical system and increased aberrations. In addition, the need of fabricating the reflecting film leads to added cost.
According to the fourth aspect of the invention, the scanning optical system of the second aspect is further characterized in that said prism member comprises three surfaces inclusive of one combined transmitting and reflecting surface.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. When a prism member is used for the second scanning optical system of the invention, it should comprise at least an entrance surface, two reflecting surfaces and an exit surface. However, if at least three surfaces, i.e., a combined surface, a transmitting surface and a reflecting surface, are used to construct the prism member, then the prism member can be simplified in construction and reduced in size.
According to the fifth aspect of the invention, there is provided a scanning optical system comprising a condensing optical system for collimating a light beam from a light source into a substantially parallel beam, optical deflection means for deflecting light emerging from said condensing optical system for scanning the surface to be scanned, and an image-formation optical system for focusing light deflected by said optical deflection means on the surface to be scanned, thereby forming an image thereon, characterized in that:
a final surface of said condensing optical system, through which a light beam leaving said condensing optical system is entered into said optical deflection means, and a first surface of said image-formation optical system, through which a light beam is entered from said optical deflection means into said image-formation optical system, are defined by the same surface.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. In forward ray tracing from the light source to the surface to be scanned, when the xe2x80x9cfinal surface that forms the condensing optical systemxe2x80x9d and the xe2x80x9cfirst surface of the image-formation optical systemxe2x80x9d, which are the surfaces located before and after the optical deflection means, are configured as separate surfaces, two such surfaces must be located at separate positions; that is, it is required to space the surface located before the optical deflection means away from the surface located after the same or increase the angle of incidence of light rays on the optical deflection means.
However, as the surfaces located before and after the optical deflection means are spaced away from each other, the size of the optical system becomes large. As the angle of incidence of light rays on the optical deflection means increases, on the other hand, the area of the optical deflection means becomes large and so makes it difficult to ensure large angles of deflection or high deflection frequencies (scanning frequencies). In particular, this offers a grave problem with optical deflection means constructed of a single reflecting surface, as is the case with a micromachined scanner fabricated making use of such micromachining as set forth in JP-A 10-20226.
If the surfaces located before and after the optical deflection means are defined by the same surface, it is then possible to make the angle of incidence of light rays on the optical deflection means so small that the area of the optical deflection means can be decreased, thereby increasing the angle of deflection of the optical deflection means or achieving high deflection frequencies (scanning frequencies).
According to the sixth aspect of the invention, the scanning optical system of the fifth aspect is further characterized in that optically functional surfaces located before and after said optical deflection means are defined by transmitting surfaces.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. In the forward ray tracing from the light source to the surface to be scanned, when the optically active surfaces located before and after the optical deflection means are defined by reflecting surfaces, both the final surface (reflecting surface 1) that forms the condensing optical system and the first surface (reflecting surface 2) that forms the image-formation optical system take the form of reflecting surfaces. In order to allow incident light on the reflecting surface 1 to arrive at that reflecting surface while unobstructed by the reflection type optical deflection means, it is necessary to increase the angle of incidence of light rays on the reflection type optical deflection means, increase the distance between the surfaces (reflecting surface 1=reflecting surface 2) located before and after the reflection type optical deflection means and the optical deflection means or make an angle between the entrance surface with respect to the optical deflection means and the primary scanning surface (both surfaces are not parallel with each other). This holds true for the case where light reflected at the reflecting surface 2 emerges while unobstructed by the reflection type optical deflection means. Whatever the case may be, however, there are several problems such as an increase in the area of the optical deflection means, an increase in the size of the optical system, and difficulty in making correction for decentration aberrations.
If the optically active surfaces located before and after the optical deflection means are configured as transmitting surfaces, then such problems can be overcome.
According to the seventh aspect of the invention, the scanning optical system of the fifth aspect is further characterized in that said image-formation optical system comprises at least one combined transmitting and reflecting surface.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. Since the two actions, transmission and reflection, occur at the same surface, the number of surfaces that form the image-formation system can be so reduced that it can be simplified in construction and reduced in size. More preferably in this case, the reflection action should be total reflection action. When reflection at the combined surface is reflection at a reflecting film rather than total reflection, it is necessary to form the reflecting film for the reflecting surface at another position separate from a transmitting area for a transmitting surface, offering problems such as an increase in the size of the optical system and increased aberrations. In addition, the need of fabricating the reflecting film leads to added cost.
According to the eighth aspect of the invention, there is provided a scanning optical system comprising a condensing optical system for collimating a light beam from a light source into a substantially parallel beam, optical deflection means for deflecting light emerging from said condensing optical system for scanning the surface to be scanned, and an image-formation optical system for focusing light deflected by said optical deflection means into the surface to be scanned, thereby forming an image thereon, characterized in that:
said scanning optical system comprises a prism member, and said prism member includes at least a portion of said condensing optical system, and at least a portion of said image-formation optical system.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. Since a portion of the condensing optical system and a portion of the image-formation optical system are configured with a single optical element, the number of parts that form the scanning optical system can be reduced. Consequently, the operation for position control on assembling for achieving the desired performance becomes easy, resulting in cost reductions.
According to the ninth aspect of the invention, the scanning optical system of the eighth aspect is further characterized in that said image-formation optical system comprises one prism member.
This scanning optical system is exemplified by Examples 1-3 and Example 6 given later.
With the ninth scanning optical system, the advantages of the eighth scanning optical system are much more enhanced.
According to the tenth aspect of the invention, a scanning optical system comprising a condensing optical system for collimating a light beam from a light source into a substantially parallel beam, optical deflection means for deflecting light emerging from said condensing optical system for scanning the surface to be scanned, and an image-formation optical system for focusing light deflected by said optical deflection means into the surface to be scanned, thereby forming an image thereon, as recited in any one of the 1st, 5th and 8th aspects of the invention is further characterized in that a total of at least three reflections occur at said condensing optical system and said image-formation optical system.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. A total of at least three reflections enhance the xe2x80x9cturn-backxe2x80x9d effect, so that the effect on reducing the overall size of the scanning optical system is much more augmented.
According to the 11th aspect of the invention, the scanning optical system of the 8th aspect is further characterized in that said prism member including at least a portion of said condensing optical system, and at least a portion of said image-formation optical system has a combined transmitting and reflecting surface.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. Since the two actions, transmission and reflection, occur at the same surface, the number of surfaces that form the optical system can be so reduced that it can be simplified construction and reduced in size. More preferably in this case, the reflection action should be total reflection action. When reflection at the combined surface is reflection at a reflecting film rather than total reflection, it is necessary to form the reflecting film for the reflecting surface at another position separate from a transmitting area for a transmitting surface, offering problems such as an increase in the size of the optical system and increased aberrations. In addition, the need of fabricating the reflecting film leads to added cost.
According to the 12th aspect of the invention, the scanning optical system of the 11th aspect is further characterized in that said prism member including at least a portion of said beam-condensing optical system, and at least a portion of said image-formation optical system has a combined transmitting and reflecting surface capable of three optical actions, i.e., two transmissions and one reflection.
This scanning optical system is exemplified by Examples 1-6 given later.
Referring to the advantages of the scanning optical system, the number of surfaces that form the scanning optical system can be much smaller than that of the 11th scanning optical system. If the surface of the prism member facing the optical deflection means is defined by such a combined surface, it is then possible to obtain the advantages of the 5th scanning optical system.
According to the 13th aspect of the invention, the 8th scanning optical system wherein said prism member comprises at least a portion of said condensing optical system, and at least a portion of said image-formation optical system is further characterized in that:
the portion of said condensing optical system included in said prism member comprises at least three surfaces, an entrance surface for said prism member, a rotationally asymmetric reflecting surface that has optical power and is decentered with respect to an axial chief ray, and an exit surface from said prism member, and
the portion of said image-formation optical system included in said prism member comprises at least three surfaces, a reentrance surface for said prism member, a rotationally asymmetric reflecting surface that has optical power and is decentered with respect to an axial chief ray, and an re-exit surface from said prism member.
This scanning optical system is exemplified by Examples 1-6 given later.
The reflecting surfaces, each having optical power, have both a lens action and a deflection action, and so are greatly effective for reducing the size of the optical system. Since both the condensing optical system and the image-formation optical system can be reduced in size, the overall size of the present scanning optical system can be reduced.
Referring here to an optical system comprising a reflecting surface having optical power and decentered with respect to an axial chief ray, light rays strike obliquely on that decentered reflecting surface. Even with axial rays, accordingly, aberrations such as comas and astigmatisms are produced due to decentration. Such decentration aberrations may be corrected by configuring this reflecting surface in the form of a rotationally asymmetric surface.
A problem with a general scanning optical system is that when light deflected by optical deflection means is entered on a decentered surface, it is impossible to ensure linear scan capability. However, this linear scan capability can be ensured by configuring the reflecting surface of an image-formation optical system in the form of a rotationally asymmetric reflecting surface. Further, the use of the rotationally asymmetric surface enables the image-formation optical system to be formed of a two-dimensional f arcsine xcex8 lens or a two-dimensional fxcex8 lens. Consequently, the surface to be scanned can be easily subjected to constant-speed scanning.
With the rotationally asymmetric reflecting surface used at the portion of the condensing optical system included in the prism member, it is possible to achieve the function of shaping beams from a light source of oval shape in section such as an LD and the function of correcting field tilts.
Generally speaking, a reflecting surface must be more strictly controlled in terms of decentration errors than a refracting surface, and so its adjustment on assembling is an onerous task. However, if the reflecting surface of the optical member is configured as one surface of the prism member, then any adjustment operation for that reflecting surface can be dispensed with.
Light rays incident from the deflection means on the portion of the image-formation optical system of the prism member are refracted at the entrance surface of the prism member, so that the heights of off-axis light rays incident on the subsequent surfaces can be kept low. It is thus possible to reduce the size of the optical system and achieve a larger angle of view as well. In addition, the heights of light rays following the off-axis light rays become so low that comas or the like can be reduced.
According to the 14th aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that the rotationally asymmetric surface of said image-formation optical system has only one symmetric plane with respect to shape.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are that the symmetric plane with respect to shape makes great contributions to productivity.
According to the 15th aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that the rotationally asymmetric surface of said beam-condensing optical system has only one symmetric plane with respect to shape.
This scanning optical system is exemplified by Examples 1-6 given later.
Referring to the advantages of the scanning optical system, the same advantages as in the 13th scanning optical system are obtained by the action and effect of the rotationally asymmetric surface, and the same advantages as in the 14th scanning optical system are obtained by the action and effect due to the incorporation of one symmetric plane with respect to shape. Thus, this embodiment is preferred in that the condensing optical system has such advantages as mentioned above.
According to the 16th aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that the rotationally asymmetric surface of said image-formation optical system is defined by a free-form surface having only one symmetric plane with respect to shape.
This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. The free-form surface used herein is defined by the following formula (a), and the axis of the free-form surface is given by the Z axis for that defining formula.                     Z        =                                            cr              2                        /                          [                              1                +                                                      {                                          1                      -                                                                        (                                                      1                            +                            k                                                    )                                                ⁢                                                  c                          2                                                ⁢                                                  r                          2                                                                                      }                                                              ⁢                              xe2x80x83                            ]                                +                                    ∑                              j                =                2                            66                        ⁢                                          C                j                            ⁢                              X                m                            ⁢                              Y                n                                                                        (        a        )            
Here the first term of formula (a) is a spherical surface term, and the second term is a free-form surface term.
In the spherical surface term, c is the curvature of an apex, K is a conic constant, and r=(X2+Y2).
The free-form surface term is                               ∑                      j            =            2                    66                ⁢                              C            j                    ⁢                      X            m                    ⁢                      Y            n                                                                                      Z              =                            ⁢                                                                    C                    2                                    ⁢                  X                                +                                                      C                    3                                    ⁢                  Y                                +                                                      C                    4                                    ⁢                                      X                    2                                                  +                                                      C                    5                                    ⁢                  XY                                +                                                      C                    6                                    ⁢                                      Y                    2                                                  +                                                      C                    7                                    ⁢                                      X                    3                                                  +                                                      C                    8                                    ⁢                                      X                    2                                    ⁢                  Y                                +                                                      C                    9                                    ⁢                                      XY                    2                                                  +                                                                                                      ⁢                                                                    C                    10                                    ⁢                                      Y                    3                                                  +                                                      C                    11                                    ⁢                                      X                    4                                                  +                                                      C                    12                                    ⁢                                      X                    3                                    ⁢                  Y                                +                                                      C                    13                                    ⁢                                      X                    2                                    ⁢                                      Y                    2                                                  +                                                      C                    14                                    ⁢                                      XY                    3                                                  +                                                      C                    15                                    ⁢                                      Y                    4                                                  +                                                      C                    16                                    ⁢                                      X                    5                                                  +                                                                                                      ⁢                                                                    C                    17                                    ⁢                                      X                    4                                    ⁢                  Y                                +                                                      C                    18                                    ⁢                                      X                    3                                    ⁢                                      Y                    2                                                  +                                                      C                    19                                    ⁢                                      X                    2                                    ⁢                                      Y                    3                                                  +                                                      C                    20                                    ⁢                                      XY                    4                                                  +                                                      C                    21                                    ⁢                                      Y                    5                                                  +                                                      C                    22                                    ⁢                                      X                    6                                                  +                                                                                                      ⁢                                                                    C                    23                                    ⁢                                      X                    5                                    ⁢                  Y                                +                                                      C                    24                                    ⁢                                      X                    4                                    ⁢                                      Y                    2                                                  +                                                      C                    25                                    ⁢                                      X                    3                                    ⁢                                      Y                    3                                                  +                                                      C                    26                                    ⁢                                      X                    2                                    ⁢                                      Y                    4                                                  +                                                      C                    27                                    ⁢                                      XY                    5                                                  +                                                      C                    28                                    ⁢                                      Y                    6                                                  +                                                                                                      ⁢                                                                    C                    29                                    ⁢                                      X                    7                                                  +                                                      C                    30                                    ⁢                                      X                    6                                    ⁢                  Y                                +                                                      C                    31                                    ⁢                                      X                    5                                    ⁢                                      Y                    2                                                  +                                                      C                    32                                    ⁢                                      X                    4                                    ⁢                                      Y                    3                                                  +                                                      C                    33                                    ⁢                                      X                    3                                    ⁢                                      Y                    4                                                  +                                                      C                    34                                    ⁢                                      X                    2                                    ⁢                                      Y                    5                                                  +                                                                                                      ⁢                                                                    C                    35                                    ⁢                                      XY                    6                                                  +                                                      C                    36                                    ⁢                                      Y                    7                                                                                          
Here Cj (j is an integer of 2 or greater) is a coefficient.
In general, the aforesaid free-form surface has no symmetric plane at both the X-Z plane and the Y-Z plane. However, by reducing all the odd-numbered terms for X to zero, that free-form surface can have only one symmetric plane parallel with the Y-Z plane. For instance, this may be achieved by reducing to zero the coefficients for the terms C2, C5, C7, C9, C12, C14, C16, C18, C20, C23, C25, C27, C29, C31, C33, C35, . . . .
By reducing all the odd-numbered terms for Y to zero, the free-form surface can have only one symmetric plane parallel with the X-Z plane. For instance, this may be achieved by reducing to zero the coefficients for the terms C3, C5, C8, C10, C12, C14, C17, C19, C21, C23, C25, C27, C30, C32, C34, C36, . . . .
By using any one of the aforesaid symmetric planes and deflecting it in that symmetric plane direction, rotationally asymmetric aberrations produced due to decentration are effectively corrected while, at the same time, productivity is improved.
It is here noted that the free-form surface may be defined by other defining formulae such as Zernike polynomial.
According to the 17th aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that said optical deflection means is defined by a single two-dimensional optical deflecting means capable of two-dimensional deflection by itself.
This scanning optical system is exemplified by Examples 1-5 given later.
The advantages of the scanning optical system are now explained. To make the area of the optical deflection means small, the optical deflection means must be located in the vicinity of the entrance pupil of the image-formation optical system. Consider the case where two one-dimensional optical deflection means are used for two-dimensional scanning. To diminish the size of the optical deflection means, the two one-dimensional deflection means must be located in conjugative relations to each other or the spacing between them must be narrowed, resulting in problems that the construction of the optical system becomes complicated and large, restrictive conditions for the layout of the optical system increase, etc. With a single optical deflection means capable of two-dimensional deflection, the optical system can be so easily laid out that it can be reduced in size and simplified in construction.
According to the 18th aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that said optical deflection means has a sinusoidally changing angle of deflection.
This scanning optical system corresponds to Examples 1, 2, 4, 5 and 6 given later as well as to Example 3 provided that electrical correction of image distortions must be made.
The advantages of the scanning optical system are now explained. For instance, a micromachined scanner fabricated making use of such micromachining as set forth in JP-A 10-20226 comprises a single reflecting mirror. Upon high-speed scanning, this reflecting mirror vibrates sinusoidally to reflect and deflect light. With such optical deflection means, not only are size and cost reductions achievable but also high-speed scanning is achievable with reduced power consumption. If, in this case, the image-formation optical system of the scanning optical system is configured in the form of an f arcsine xcex8 lens, it is then possible to carry out constant-speed scanning for the surface to be scanned.
According to the 19th aspect of the invention, the scanning optical system of the 18th aspect is further characterized in that said optical deflection means having a sinusoidally changing angle of deflection is capable of using up to 95% of the amplitude of an angle of deflection of light for scanning.
This scanning optical system corresponds to Examples 1, 2, 4, 5 and 6 given later as well as to Example 3 provided that electrical correction of image distortions must be made.
The advantages of the scanning optical system are now explained with reference to a reflection type deflector such as a galvanometer mirror. As shown in FIG. 9(a), consider the case where there is used a reflection type deflector (reflection type deflection means) wherein the deflection angle xcex8 of its reflecting surface from a reference reflecting surface changes sinusoidally. To carry out constant-speed scanning without recourse to any electrical correction of image distortions, it is then required that the image-formation optical system be configured in the form of an f arcsine xcex8 lens.
Here assume that with deflecting means wherein the deflection angle of its reflecting surface changes sinusoidally at an amplitude xcfx860/k, the surface to be scanned is scanned making use of a deflection angle (xc2x1xcfx860) that is k times as large as the amplitude of the deflection angle of the reflecting surface. To configure the image-formation optical system in the form of an f arcsine xcex8 lens, it is then required to satisfy the following condition (0 less than kxe2x89xa6xe2x88x921):
Image Height y=fxc2x72(xcfx860/k)arcsin{xcfx86/(xcfx860/k)}
To configure the image-formation system in the form of an f arcsine xcex8 lens well fit for the whole range of an angle of deflection of about xc2x120xc2x0, it is necessary to produce some considerable plus distortions, rendering the design of the image-formation system difficult. By making use of only an area where the linearity of xcfx86/(xcfx860/k) is better, however, it is easy to configure the image-formation system as an f arcsine xcex8 lens.
At kxe2x89xa60.95, the linearity of xcfx86/(xcfx860/k) is at most about half that in the case of k=1, so that it is easy to configure the image-formation optical system as an f arcsine xcex8 lens. It is thus possible to simplify the optical system with size reductions.
As is the case of a conventional display having a blanking interval of the order of 17%, a scanning optical system, too, cannot utilize the whole range of the angle of deflection by reason of electrical processing. In the present invention, however, the upper limit to the amplitude of the angle of deflection of the deflection means is about 95% because images can be displayed without recourse to an ordinary display.
As shown in FIG. 9(b), the foregoing explanation goes true for a transmission type of optical deflection means such as an acousto-optic deflector ADO; however, it is noted that the angle of deflection is given by 2xcfx86.
According to the 20th aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that constant-speed scan capability is electrically corrected.
This scanning optical system may be embodied as desired.
The advantages of the 20th scanning optical system are now explained. Especially when, on two-dimensional scanning, two-dimensional linear scan capability and constant-speed scan capability are ensured by allowing the image-formation optical system to produce suitable distortion in conformity with the deflection characteristics of the optical deflection means, the scanning optical system becomes complicated and large. On two-dimensional scanning at high speed, on the other hand, it is difficult to make electrical, real-time correction for image distortions due to linear scan capability, because that correction is two-dimensional one.
If the linear scan capability is ensured by the image-formation optical system and constant-speed scan capability is done by electrical correction, then the scanning optical system can be simplified in construction and reduced in size. In addition, the scanning optical system is compatible with high-speed scanning because the image distortions can be electrically corrected per scanning line in the main scanning direction.
In this case, when all of the amplitude of the sinusoidally changing angle of deflection is harnessed, there is too large a scanning speed difference between in the vicinity of the center of an image to be scanned at high speed and in the vicinity of the periphery of an image to be scanned at low speed. Consequently, even when electrical correction of image distortions is made, it is difficult to make that correction with high precision. It is thus preferable to make use of about 85% of the amplitude of the angle of deflection, because correction of the constant-speed scan capability is improved in approximately two steps.
According to the 21st aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that the angle of deflection by said optical deflecting means changes linearly.
This scanning optical system is exemplified by Example 3 given later (and corresponds to Examples 1, 2 and 4-6, too, with the proviso that image distortions are electrically corrected).
The advantages of the scanning optical system are now explained. The rotary polygon mirror rotates at a constant speed, and so the angle of optical deflection changes linearly. If the rotary polygon mirror is used as optical deflection means, it is then possible to ensure a large angle of deflection with that optical deflection means and make the field angle of the scanning optical system large. At this time, if an fxcex8 lens is used as the image-formation optical system for the scanning optical system, the surface to be scanned can then be scanned at a constant speed.
According to the 22nd aspect of the invention, the scanning optical system of any one of the 1st, 5th and 8th aspects is further characterized in that said-image formation optical system has only one symmetric plane with respect to shape and is decentered only in said symmetric plane with respect to plane, said scanning optical system satisfying the following formula:
xcfx862xcex81/xcfx861xcex82 less than 1xe2x80x83xe2x80x83(1) 
Here xcex82 is the half field angle of the image-formation optical system in a symmetric plane direction on the side of the surface to be scanned, xcex81 is the half field angle of the image-formation optical system in a plane direction perpendicular to the symmetric plane, 2xcfx862 is the one-side angle of deflection of the optical deflecting means needed for scanning of the surface to be scanned in the symmetric plane direction, and 2xcfx861 is the one-side angle of deflection of the optical deflecting means necessary for scanning of the surface to be scanned in a plane direction perpendicular to the symmetric plane.
This formula indicates that when it comes down to such reflection type deflecting means as a polygon or galvanometer mirror, the one-side deflection angle of the reflecting mirror necessary for scanning is given by xcfx861, and xcfx862. The one-side deflection angle of the reflecting mirror, used herein, is understood to refer to a maximum angle of deviation from the surface of the reflecting mirror corresponding to the center of the surface to be scanned; however, this does not always mean that the optical deflection means, i.e., the reflecting mirror deflects xc2x1xcfx86. To put it another way, when a part of the amplitude of the reflecting mirror is used to scan the surface to be scanned, the deflection angle used therefor is xc2x1xcfx86. For such a transmission type of optical deflecting means as an acousto-optical deflector AOD, the one-side angle of deflection is represented by 2xcfx861 and 2xcfx862 (see FIG. 9). This scanning optical system is exemplified by Examples 1-6 given later.
The advantages of this scanning optical system are now explained with reference to such a reflection type of optical deflection means as a polygon or galvanometer mirror (see FIG. 9(a)). Here assume that when the one-side deflection angle of the reflection type optical deflection means is xcfx86 (or when the angle of deflection is 2xcfx86), the half field angle on scanning of the image-formation optical system is xcex8. Then, the pupil magnification of the image-formation optical system upon forward ray tracing is given by 2xcfx86/xcex8.
As already set forth herein, it is preferable that the image-formation optical system has only one symmetric plane with respect to shape, and is decentered in that symmetric plane alone, because the productivity of the image-formation optical system is improved with cost reductions. In this case, it is easy to ensure a wide field angle in the direction vertical to the symmetric plane with respect to shape, and so it is desired that this direction be determined as the scanning direction of a one-dimensional scanning optical system or as a direction in which the scanning field angle of a two-dimensional optical system becomes large. It is then noted that the image-formation optical system is difficult to construct, because the optical system must be designed in such a way that the decentered surface of the image-formation optical system does not interfere with the rest in the plane direction in which the image-formation optical system is decentered.
To remove such difficulty, it is preferable that the pupil magnification of the image-formation optical system in the direction in which it is decentered (in the symmetric plane direction of the image-formation optical system with respect to shape) is smaller than that in the direction vertical to the symmetric plane, thereby reducing the beam spread angle in the image-formation optical system, because it is easier to construct the image-formation optical system.
More specifically, it is desired to satisfy the following formula:       1     greater than           pupil      ⁢              xe2x80x83            ⁢      magnification      ⁢              xe2x80x83            ⁢      in      ⁢              xe2x80x83            ⁢      the      ⁢              xe2x80x83            ⁢      symmetric      ⁢              xe2x80x83            ⁢              plane        /        pupil            ⁢              xe2x80x83            ⁢      magnification      ⁢              xe2x80x83            ⁢      in      ⁢              xe2x80x83            ⁢      the      ⁢              xe2x80x83            ⁢      plane      ⁢              xe2x80x83            ⁢      vertical      ⁢              xe2x80x83            ⁢      to      ⁢              xe2x80x83            ⁢      the      ⁢              xe2x80x83            ⁢      symmetric      ⁢              xe2x80x83            ⁢      plane        =                    (                  2          ⁢                      xe2x80x83                    ⁢                                    φ              2                        /                          θ              2                                      )            /              (                  2          ⁢                      xe2x80x83                    ⁢                                    φ              1                        /                          θ              1                                      )              =                  φ        2            ⁢                        θ          1                /                  φ          1                    ⁢              θ        2            
When the symmetric plane direction of the image-formation optical system with respect to shape is determined as the sub-scanning direction and the direction vertical to the symmetric plane as the main scanning direction, the resolving power of the image-formation optical system in the main scanning direction must be made equal to that in the sub-scanning direction by making the size of the optical deflection means in the sub-scanning direction larger than that in the main scanning direction. This image-formation optical system is well compatible with high-speed scanning because of a decrease in its size in the main scanning direction in which high-speed scanning is necessary for two-dimensional scanning.
According to the 23rd aspect of the invention, the scanning optical system of the 22nd aspect is further characterized by satisfying the following condition:
NA2/NA1 greater than 1xe2x80x83xe2x80x83(2) 
Here NA2 is the numerical aperture of a light beam that is incident from the light source in the symmetric plane direction with respect to shape on the condensing optical system, and NA1 is the numerical aperture of a light beam that is incident from the light source in the direction vertical to the symmetric plane with respect to shape on the condensing optical system.
This scanning optical system is embodied by Examples 1-6 given later.
The advantages of the scanning optical system are now explained. When the symmetric plane direction of the image-formation optical system with respect to shape is determined as the sub-scanning direction and the direction vertical to the symmetric plane as the main scanning direction, the resolving power of the image-formation optical system in the main scanning direction must be made equal to that in the sub-scanning direction by making the size of the optical deflection means in the sub-scanning direction larger than that in the main scanning direction.
In order that the light leaving the light source has the aforesaid shape at the scanning means, it is preferable to satisfy condition (2) because the condensing optical system is easier to construct.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification.
The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims.